Finite Group Databasebeta

← #13072034

Subgroups — #13072034

Order 1408.

704 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C11C211yesmaximal, characteristic, complemented
2C2×#66983C211yesmaximal, characteristic, complemented
3C2×#66983C211yesmaximal, characteristic, complemented
4C2×#66979C211yesmaximal, characteristic, complemented
5#10622836C212yesmaximal, complemented
6#10622825C211yesmaximal, characteristic, complemented
7#10622603C212yesmaximal, complemented
8#10622572C212yesmaximal, complemented
9#10622570C212yesmaximal, complemented
10#10622552C211yesmaximal, characteristic, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2212yes—
17C22×D44C2211yescharacteristic
18C4×D4×C11—24no—
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×C22⋊Dic11C2212yes—
24C2×C22⋊Dic11C2212yes—
25#66983—24no—
26#66983—24no—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×(C2×D11)⋊C4C2212yes—
31#66979—24no—
32C2×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊Dic11C2211yescharacteristic
35C2×Dic11⋊C4C2212yes—
36C2×C4×Dic11C2212yes—
37C11⋊#95C2212yes—
38C11⋊#95C2212yes—
39C24×C11C2311yescharacteristic
40C24×C11C2311yescharacteristic
41C23×D11C2312yes—
42C2×D4×C11—22no—
43C2×D4×C11—22no—
44C2×D4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11D414yescomplemented
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C2×C22⋊D11—24no—
57C2×C22⋊D11—24no—
58C2×C22⋊D11—24no—
59C2×C22⋊D11—42no—
60C2×C22⋊D11—42no—
61C2×C22⋊D11—42no—
62C22×Dic11C2312yes—
63C22×Dic11C2312yes—
64C22×Dic11C2312yes—
65C2×D44—22no—
66C2×D44—22no—
67C2×D44—22no—
68C11×C4⋊C4—22no—
69C11×C22⋊C4—22no—
70C11×C22⋊C4—22no—
71C42×C11—22no—
72C22⋊Dic11—24no—
73C22⋊Dic11—42no—
74(C2×D11)⋊C4—24no—
75(C2×D11)⋊C4—24no—
76(C2×D11)⋊C4—24no—
77(C2×D11)⋊C4—42no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80C4⋊Dic11D414yescomplemented
81Dic11⋊C4—42no—
82C4×Dic11—24no—
83#2414—111nomaximal, Sylow
84C23×C11—21no—
85C23×C11—21no—
86C23×C11—21no—
87C23×C11—21no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—21no—
95C23×C11—21no—
96C23×C11C2×D412yes—
97C23×C11#4112yes—
98C23×C11C2411yescharacteristic
99C22×D11—22no—
100C22×D11—22no—
101C22×D11—22no—
102C22×D11—22no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—22no—
106D4×C11—28no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—28no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—44no—
119C2×C4×C11C2×D412yes—
120C2×C4×C11C2×D412yes—
121C2×C4×C11C2×D412yes—
122C2×C4×C11#4112yes—
123C2×C4×C11#4112yes—
124C22⋊D11—48no—
125C22⋊D11—48no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—22no—
133C2×Dic11—22no—
134C2×Dic11C2×D414yes—
135D44—44no—
136C2×#121—111no—
137C2×#121—111no—
138C2×C4×D4D1111yescharacteristic, complemented
139C2×#117—111no—
140#394—112no—
141#392—112no—
142#390—112no—
143#390—111no—
144#389—111no—
145#388—112no—
146#380—111no—
147C22×C11—22no—
148C22×C11—22no—
149C22×C11—22no—
150C22×C11—22no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—41no—
156C22×C11—41no—
157C22×C11—41no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11C22×D411yescharacteristic
162C22×C11C22×D411yescharacteristic
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C22×C11C2×#4111yescharacteristic
166C22×C11H(5,𝔽2)11yescharacteristic
167C22×C11H(5,𝔽2)11yescharacteristic
168C2×D11—42no—
169C2×D11—42no—
170C2×D11—42no—
171C2×D11—42no—
172C2×D11—42no—
173C2×D11—42no—
174C2×D11—42no—
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11#12114yes—
180Dic11—24no—
181Dic11—42no—
182Dic11—42no—
183C22×D4—112no—
184C22×D4—112no—
185C22×D4—111no—
186C22×D4C2×D1111yescharacteristic
187C23×C4C2×D1111yescharacteristic
188C23×C4C2×D1111yescharacteristic
189#121—224no—
190#121—224no—
191C4×D4—24no—
192#117—224no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—112no—
197C2×C4⋊C4C2×D1111yescharacteristic
198C2×C22⋊C4—112no—
199C2×C22⋊C4—112no—
200C2×C22⋊C4—112no—
201C2×C22⋊C4—112no—
202C2×C22⋊C4—112no—
203C2×C22⋊C4—112no—
204C2×C22⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4C2×D1111yescharacteristic
206C2×C42—112no—
207C2×C42C2×D1111yescharacteristic
208#95—112no—
209#95—112no—
210C2×C11—42no—
211C2×C11—42no—
212C2×C11C2×#12111yescharacteristic
213C2×C11#52511yescharacteristic
214C2×C11#53511yescharacteristic
215C2×C11#54611yescharacteristic
216C2×C11#55011yescharacteristic
217C2×C11#55311yescharacteristic
218C2×C11#55511yescharacteristic
219D11—82no—
220C24—112no—
221C24C22×D1111yescharacteristic
222C24C22×D1111yescharacteristic
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—224no—
227C2×D4—224no—
228C2×D4—224no—
229C2×D4—222no—
230C2×D4—222no—
231C2×D4—222no—
232C2×D4—442no—
233C2×D4—442no—
234C2×D4—442no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—112no—
241C22×C4—112no—
242C22×C4—112no—
243C22×C4C22⋊D1114yescomplemented
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C22×C4C22×D1111yescharacteristic
248C22×C4C22×D1111yescharacteristic
249C4⋊C4—22no—
250C4⋊C4—114no—
251C4⋊C4—222no—
252C4⋊C4—222no—
253C4⋊C4—442no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—224no—
257C22⋊C4—224no—
258C22⋊C4—224no—
259C22⋊C4—224no—
260C22⋊C4—442no—
261C22⋊C4—442no—
262C42—22no—
263C42—224no—
264C11#241411yescharacteristic, complemented, Sylow
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—222no—
278C23—222no—
279C23—222no—
280C23—222no—
281C23—222no—
282C23—222no—
283C23—222no—
284C23#433912yes—
285C23C2×C22⋊D1112yes—
286C23C23×D1111yescharacteristic
287D4—28no—
288D4—448no—
289D4—448no—
290D4—444no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—28no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—44no—
303C2×C4—114no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4#433912yes—
313C2×C4D4×D1112yes—
314C2×C4#434112yes—
315C2×C4C2×C22⋊D1112yes—
316C2×C4C2×C22⋊D1112yes—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—442no—
332C22—442no—
333C22—442no—
334C22—442no—
335C22—442no—
336C22—442no—
337C22—442no—
338C22C2×#433911yescharacteristic
339C22C2×#433911yescharacteristic
340C22C2×D4×D1111yescharacteristic
341C22C2×#434111yescharacteristic
342C22#6704211yescharacteristic
343C22#6704211yescharacteristic
344C22C22×C22⋊D1111yescharacteristic
345C4—22no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—224no—
350C4—442no—
351C4—442no—
352C4#6699214yes—
353C2—42no—
354C2—42no—
355C2—882no—
356C2#1062308111yescharacteristic
357C2#1062308411yescharacteristic
358C2#1062309411yescharacteristic
359C2#1062309611yescharacteristic
360C2#1062332211yescharacteristic
361C2C2×#6699211yescharacteristic
362C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
hypercenterC2×C4×D4D11
hypocenterC11#2414
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C4×D4×C11C2semidirect
2. C2×#66983C2semidirect
3. C2×#66983C2semidirect
4. C2×#66979C2semidirect
5. #10622836C2semidirect
6. #10622825C2semidirect
7. #10622603C2semidirect
8. #10622572C2semidirect
9. #10622570C2semidirect
10. #10622552C2semidirect
11. #10622541C2semidirect
50. C22×C4×C11D4semidirect
80. C4⋊Dic11D4semidirect
138. C2×C4×D4D11semidirect
243. C22×C4C22⋊D11semidirect
264. C11#2414semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×D4×C112
C2×#669832
C2×#669792
#106228362
#106228252
#106226032
#106225722
#106225702
#106225522
#106225412
#241411